论文标题
基于多个傅里叶 - legendre串联的统一泰勒-Ito扩展的迭代ITO随机积分的均方体近似程序的优化。
Optimization of the Mean-Square Approximation Procedures for Iterated Ito Stochastic Integrals of Multiplicities 1 to 5 from the Unified Taylor-Ito Expansion Based on Multiple Fourier-Legendre Series
论文作者
论文摘要
The article is devoted to optimization of the mean-square approximation procedures for iterated Ito stochastic integrals of multiplicities 1 to 5. The mentioned stochastic integrals are part of strong numerical methods with convergence orders 1.0, 1.5, 2.0, and 2.5 for Ito stochastic differential equations with multidimensional non-commutative noise based on the unified Taylor-Ito expansion and multiple Fourier-Legendre series Hilbert Space $ L_2（[T，T]^K）$ $（k = 1，\ ldots，5）。$在本文中，我们在本文中使用多个傅立叶 - legendre系列，这是在扩展方法和均值均值近似的框架内，基于迭代的ITO定型积分基于常规多个傅立叶量。我们表明，独立标准高斯随机变量的序列长度是迭代迭代的迭代iTO随机积分1至5的均值近似所需的均值，而无需损失这些随机积分的均值近似准确性。
The article is devoted to optimization of the mean-square approximation procedures for iterated Ito stochastic integrals of multiplicities 1 to 5. The mentioned stochastic integrals are part of strong numerical methods with convergence orders 1.0, 1.5, 2.0, and 2.5 for Ito stochastic differential equations with multidimensional non-commutative noise based on the unified Taylor-Ito expansion and multiple Fourier-Legendre series converging in the sense of norm in Hilbert space $L_2([t, T]^k)$ $(k=1,\ldots,5).$ In this article we use multiple Fourier-Legendre series within the framework of the method of expansion and mean-square approximation of iterated Ito stochastic integrals based on generalized multiple Fourier series. We show that the lengths of sequences of independent standard Gaussian random variables required for the mean-square approximation of iterated Ito stochastic integrals of multiplicities 1 to 5 can be significantly reduced without the loss of the mean-square accuracy of approximation for these stochastic integrals.
